Graph y=tan(x/2)

Problem

y=tan(x/2)

Solution

1. Identify the parent function and its properties. The function is a transformation of y=tan(x) which has a period of π and vertical asymptotes at x=π/2+n*π

2. Determine the period of the transformed function. The period P is calculated by dividing the standard period of tangent by the coefficient of x

P=π/(1/2)

P=2*π

3. Find the vertical asymptotes by setting the argument of the tangent function equal to the standard asymptote locations.

x/2=π/2+n*π

x=π+2*n*π

For n=0 there is an asymptote at x=π For n=−1 there is an asymptote at x=−π

4. Identify key points within one period (−π,π)
   When x=0 y=tan(0)=0
   When x=π/2 y=tan(π/4)=1
   When x=−π/2 y=tan(−π/4)=−1

5. Sketch the graph by plotting the center point (0,0) the key points (π/2,1) and (−π/2,−1) and drawing the curves approaching the vertical asymptotes at x=±π

Final Answer

y=tan(x/2)* has period *2*π* and asymptotes at *x=π+2*n*π

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